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                <h1 id="线段树"><a href="#线段树" class="headerlink" title="线段树"></a>线段树</h1><h2 id="动态开点"><a href="#动态开点" class="headerlink" title="动态开点"></a>动态开点</h2><p><img src="https://img-blog.csdnimg.cn/69e5c9f3080547aa8212e9f29dcab37c.png" alt="在这里插入图片描述"></p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e7</span>+<span class="number">5e6</span>+<span class="number">10</span>;</span><br><span class="line"><span class="type">int</span> ls[N],rs[N],root,sum[N],idx,lazy[N];</span><br><span class="line"><span class="type">int</span> n,q,ql,qr,k;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    sum[u]=sum[ls[u]]+sum[rs[u]];</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(lazy[u]==<span class="number">-1</span>)<span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">if</span>(!ls[u])ls[u]=++idx;</span><br><span class="line">    <span class="keyword">if</span>(!rs[u])rs[u]=++idx;</span><br><span class="line">    lazy[ls[u]]=lazy[rs[u]]=lazy[u];</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    sum[ls[u]]=(mid-l+<span class="number">1</span>)*lazy[u];</span><br><span class="line">    sum[rs[u]]=(r-mid)*lazy[u];</span><br><span class="line">    lazy[u]=<span class="number">-1</span>;</span><br><span class="line">    <span class="comment">//动态开点的结点是不能写成递归的形式，要确切给定操作区间</span></span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">modify</span><span class="params">(<span class="type">int</span> &amp;u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr,<span class="type">int</span> k)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(!u)u=++idx;</span><br><span class="line">    <span class="keyword">if</span>(r&lt;ql||l&gt;qr)<span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr){</span><br><span class="line">        sum[u]=(r-l+<span class="number">1</span>)*k;</span><br><span class="line">        lazy[u]=k;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">pushdown</span>(u,l,r);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)<span class="built_in">modify</span>(ls[u],l,mid,ql,qr,k);</span><br><span class="line">    <span class="keyword">if</span>(qr&gt;mid)<span class="built_in">modify</span>(rs[u],mid+<span class="number">1</span>,r,ql,qr,k);</span><br><span class="line">    <span class="built_in">pushup</span>(u);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);cin.<span class="built_in">tie</span>(<span class="number">0</span>);cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cin&gt;&gt;n&gt;&gt;q;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">0</span>;i&lt;N;i++)lazy[i]=<span class="number">-1</span>;</span><br><span class="line">    <span class="built_in">modify</span>(root,<span class="number">1</span>,n,<span class="number">1</span>,n,<span class="number">0</span>);</span><br><span class="line">    <span class="comment">//根节点为root的点占据的区间是1-n</span></span><br><span class="line">    <span class="comment">//这个操作是把【1，n】这个区间推平为0</span></span><br><span class="line">    <span class="keyword">while</span>(q--){</span><br><span class="line">        cin&gt;&gt;ql&gt;&gt;qr&gt;&gt;k;</span><br><span class="line">        <span class="built_in">modify</span>(root,<span class="number">1</span>,n,ql,qr,<span class="number">2</span>-k);</span><br><span class="line">        cout&lt;&lt;n-sum[root]&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">    }</span><br><span class="line">    </span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>

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<h2 id="把边权化为点权"><a href="#把边权化为点权" class="headerlink" title="把边权化为点权"></a>把边权化为点权</h2><p><img src="https://img-blog.csdnimg.cn/5c4fce11116f4c9185be96ca3e690d22.png" alt="在这里插入图片描述"><br><img src="https://img-blog.csdnimg.cn/3770161ac3014d808af997da8998444f.png" alt="在这里插入图片描述"></p>
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class="line">182</span><br><span class="line">183</span><br><span class="line">184</span><br><span class="line">185</span><br><span class="line">186</span><br><span class="line">187</span><br><span class="line">188</span><br><span class="line">189</span><br><span class="line">190</span><br><span class="line">191</span><br><span class="line">192</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span>+<span class="number">10</span>,M=<span class="number">2</span>*N;</span><br><span class="line"><span class="type">int</span> h[N],e[M],ne[M],w[M],idx,cnt,fa[N],top[N],nw[N],dep[N],tmp[N];</span><br><span class="line"><span class="type">int</span> id[N],sz[N],son[N];</span><br><span class="line"><span class="keyword">typedef</span> pair&lt;<span class="type">int</span>, <span class="type">int</span>&gt; PII;</span><br><span class="line">PII ab[N];</span><br><span class="line"><span class="type">int</span> n,x,y,a,b,c,m;</span><br><span class="line">string op;</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">    <span class="type">int</span> sum,max,min,lazy;</span><br><span class="line">}t[N*<span class="number">4</span>];</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">add</span><span class="params">(<span class="type">int</span> a,<span class="type">int</span> b,<span class="type">int</span> c)</span></span>{</span><br><span class="line">    e[++idx]=b,w[idx]=c,ne[idx]=h[a],h[a]=idx;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">dfs1</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> father)</span></span>{</span><br><span class="line">    dep[u]=dep[father]+<span class="number">1</span>,fa[u]=father,sz[u]=<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=h[u];i;i=ne[i]){</span><br><span class="line">        <span class="type">int</span> j=e[i];</span><br><span class="line">        <span class="keyword">if</span>(j==father)<span class="keyword">continue</span>;</span><br><span class="line">        <span class="built_in">dfs1</span>(j,u);</span><br><span class="line">        tmp[j]=w[i];</span><br><span class="line">        sz[u]+=sz[j];</span><br><span class="line">        <span class="keyword">if</span>(sz[son[u]]&lt;sz[j])son[u]=j;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">dfs2</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> t)</span></span>{</span><br><span class="line">    id[x]=++cnt,nw[cnt]=tmp[x],top[x]=t;</span><br><span class="line">    <span class="keyword">if</span>(son[x])<span class="built_in">dfs2</span>(son[x],t);</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=h[x];i;i=ne[i]){</span><br><span class="line">        <span class="type">int</span> j=e[i];</span><br><span class="line">        <span class="keyword">if</span>(j==fa[x]||j==son[x])<span class="keyword">continue</span>;</span><br><span class="line">        <span class="built_in">dfs2</span>(j,j);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    t[u].sum=t[u&lt;&lt;<span class="number">1</span>].sum+t[u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>].sum;</span><br><span class="line">    t[u].max=<span class="built_in">max</span>(t[u&lt;&lt;<span class="number">1</span>].max,t[u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>].max);</span><br><span class="line">    t[u].min=<span class="built_in">min</span>(t[u&lt;&lt;<span class="number">1</span>].min,t[u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>].min);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(t[u].lazy==<span class="number">0</span>)<span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">auto</span> &amp;L=t[u&lt;&lt;<span class="number">1</span>];</span><br><span class="line">    <span class="keyword">auto</span> &amp;R=t[u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>];</span><br><span class="line">    L.lazy^=<span class="number">1</span>,R.lazy^=<span class="number">1</span>;</span><br><span class="line">    L.sum=-L.sum,L.max=-L.max,L.min=-L.min;</span><br><span class="line">    R.sum=-R.sum,R.max=-R.max,R.min=-R.min;</span><br><span class="line">    <span class="built_in">swap</span>(L.max,L.min),<span class="built_in">swap</span>(R.max,R.min);</span><br><span class="line">    t[u].lazy=<span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">build</span><span class="params">(<span class="type">int</span> u=<span class="number">1</span>,<span class="type">int</span> l=<span class="number">1</span>,<span class="type">int</span> r=n)</span></span>{</span><br><span class="line">    t[u]={nw[l],nw[l],nw[l]};</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=r)<span class="keyword">return</span>;</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="built_in">build</span>(u&lt;&lt;<span class="number">1</span>,l,mid),<span class="built_in">build</span>(u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>,mid+<span class="number">1</span>,r);</span><br><span class="line">    <span class="built_in">pushup</span>(u);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">modify</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> i,<span class="type">int</span> k)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(l==r){</span><br><span class="line">        t[u].sum=t[u].max=t[u].min=k;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">if</span>(i&lt;=mid)<span class="built_in">modify</span>(u&lt;&lt;<span class="number">1</span>,l,mid,i,k);</span><br><span class="line">    <span class="keyword">else</span> <span class="built_in">modify</span>(u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>,mid+<span class="number">1</span>,r,i,k);</span><br><span class="line">    <span class="built_in">pushup</span>(u);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">update</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr,<span class="type">int</span> lazy=<span class="number">1</span>)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(l&gt;qr||r&lt;ql)<span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr){</span><br><span class="line">        t[u].sum=-t[u].sum;</span><br><span class="line">        t[u].max=-t[u].max;</span><br><span class="line">        t[u].min=-t[u].min;</span><br><span class="line">        <span class="built_in">swap</span>(t[u].max,t[u].min);</span><br><span class="line">        t[u].lazy^=<span class="number">1</span>;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)<span class="built_in">update</span>(u&lt;&lt;<span class="number">1</span>,l,mid,ql,qr);</span><br><span class="line">    <span class="keyword">if</span>(qr&gt;mid)<span class="built_in">update</span>(u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>,mid+<span class="number">1</span>,r,ql,qr);</span><br><span class="line">    <span class="built_in">pushup</span>(u);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qmax</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(l&gt;qr||r&lt;ql)<span class="keyword">return</span> <span class="number">-1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr)<span class="keyword">return</span> t[u].max;</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">-1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)ans=<span class="built_in">max</span>(ans,<span class="built_in">qmax</span>(u&lt;&lt;<span class="number">1</span>,l,mid,ql,qr));</span><br><span class="line">    <span class="keyword">if</span>(qr&gt; mid)ans=<span class="built_in">max</span>(ans,<span class="built_in">qmax</span>(u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>,mid+<span class="number">1</span>,r,ql,qr));</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qmin</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(l&gt;qr||r&lt;ql)<span class="keyword">return</span> <span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr)<span class="keyword">return</span> t[u].min;</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)ans=<span class="built_in">min</span>(ans,<span class="built_in">qmin</span>(u&lt;&lt;<span class="number">1</span>,l,mid,ql,qr));</span><br><span class="line">    <span class="keyword">if</span>(qr&gt; mid)ans=<span class="built_in">min</span>(ans,<span class="built_in">qmin</span>(u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>,mid+<span class="number">1</span>,r,ql,qr));</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qsum</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(l&gt;qr||r&lt;ql)<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr)<span class="keyword">return</span> t[u].sum;</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)ans+=<span class="built_in">qsum</span>(u&lt;&lt;<span class="number">1</span>,l,mid,ql,qr);</span><br><span class="line">    <span class="keyword">if</span>(qr&gt; mid)ans+=<span class="built_in">qsum</span>(u&lt;&lt;<span class="number">1</span>|<span class="number">1</span>,mid+<span class="number">1</span>,r,ql,qr);</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="comment">/* 上面是线段树，下面是树链剖分*/</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">update</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line">        <span class="keyword">if</span>(dep[top[x]]&lt;dep[top[y]])<span class="built_in">swap</span>(x,y);</span><br><span class="line">        <span class="built_in">update</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[top[x]],id[x]);</span><br><span class="line">        x=fa[top[x]];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(dep[x]&gt;dep[y])<span class="built_in">swap</span>(x,y);</span><br><span class="line">    <span class="keyword">if</span>(x!=y)<span class="built_in">update</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[x]+<span class="number">1</span>,id[y]);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qmax</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">-1e9</span>;</span><br><span class="line">    <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line">        <span class="keyword">if</span>(dep[top[x]]&lt;dep[top[y]])<span class="built_in">swap</span>(x,y);</span><br><span class="line">        ans=<span class="built_in">max</span>(ans, <span class="built_in">qmax</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[top[x]],id[x]) );</span><br><span class="line">        x=fa[top[x]];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(dep[x]&gt;dep[y])<span class="built_in">swap</span>(x,y);</span><br><span class="line">    <span class="keyword">if</span>(x!=y)ans=<span class="built_in">max</span>(ans,<span class="built_in">qmax</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[x]+<span class="number">1</span>,id[y]));</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qmin</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line">        <span class="keyword">if</span>(dep[top[x]]&lt;dep[top[y]])<span class="built_in">swap</span>(x,y);</span><br><span class="line">        ans=<span class="built_in">min</span>(ans, <span class="built_in">qmin</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[top[x]],id[x]));</span><br><span class="line">        x=fa[top[x]];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(dep[x]&gt;dep[y])<span class="built_in">swap</span>(x,y);</span><br><span class="line">    <span class="keyword">if</span>(x!=y)ans=<span class="built_in">min</span>(ans,<span class="built_in">qmin</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[x]+<span class="number">1</span>,id[y]));</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qsum</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line">        <span class="keyword">if</span>(dep[top[x]]&lt;dep[top[y]])<span class="built_in">swap</span>(x,y);</span><br><span class="line">        ans+=<span class="built_in">qsum</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[top[x]],id[x]);</span><br><span class="line">        x=fa[top[x]];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(dep[x]&gt;dep[y])<span class="built_in">swap</span>(x,y);</span><br><span class="line">    <span class="keyword">if</span>(x!=y)ans+=<span class="built_in">qsum</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[x]+<span class="number">1</span>,id[y]);</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);</span><br><span class="line">    cin.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cin&gt;&gt;n;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;n;i++){</span><br><span class="line">        cin&gt;&gt;a&gt;&gt;b&gt;&gt;c;</span><br><span class="line">        a++,b++;</span><br><span class="line">        ab[i]={a,b};</span><br><span class="line">        <span class="built_in">add</span>(a,b,c);</span><br><span class="line">        <span class="built_in">add</span>(b,a,c);</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">dfs1</span>(<span class="number">1</span>,<span class="number">0</span>);</span><br><span class="line">    <span class="built_in">dfs2</span>(<span class="number">1</span>,<span class="number">1</span>);</span><br><span class="line">    <span class="built_in">build</span>(<span class="number">1</span>,<span class="number">1</span>,n);</span><br><span class="line">    cin&gt;&gt;m;</span><br><span class="line">    <span class="keyword">while</span>(m--){</span><br><span class="line">        cin&gt;&gt;op&gt;&gt;x&gt;&gt;y;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"C"</span>){</span><br><span class="line">            <span class="type">int</span> a=ab[x].first;</span><br><span class="line">            <span class="type">int</span> b=ab[x].second;</span><br><span class="line">            <span class="keyword">if</span>(dep[a]&lt;dep[b])<span class="built_in">swap</span>(a,b);</span><br><span class="line">            <span class="built_in">modify</span>(<span class="number">1</span>,<span class="number">1</span>,n,id[a],y);</span><br><span class="line">            <span class="keyword">continue</span>;</span><br><span class="line">        }</span><br><span class="line">        x++,y++;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"N"</span>)<span class="built_in">update</span>(x,y);</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"SUM"</span>)cout&lt;&lt;<span class="built_in">qsum</span>(x,y)&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"MAX"</span>)cout&lt;&lt;<span class="built_in">qmax</span>(x,y)&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"MIN"</span>)cout&lt;&lt;<span class="built_in">qmin</span>(x,y)&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>

<p>拓展</p>
<p>如果是在有颜色的树上修改呢</p>
<p>颜色个数为1e5</p>
<p>也就是说这道题要动态开点来写</p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span 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class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br><span class="line">146</span><br><span class="line">147</span><br><span class="line">148</span><br><span class="line">149</span><br><span class="line">150</span><br><span class="line">151</span><br><span class="line">152</span><br><span class="line">153</span><br><span class="line">154</span><br><span class="line">155</span><br><span class="line">156</span><br><span class="line">157</span><br><span class="line">158</span><br><span class="line">159</span><br><span class="line">160</span><br><span class="line">161</span><br><span class="line">162</span><br><span class="line">163</span><br><span class="line">164</span><br><span class="line">165</span><br><span class="line">166</span><br><span class="line">167</span><br><span class="line">168</span><br><span class="line">169</span><br><span class="line">170</span><br><span class="line">171</span><br><span class="line">172</span><br><span class="line">173</span><br><span class="line">174</span><br><span class="line">175</span><br><span class="line">176</span><br><span class="line">177</span><br><span class="line">178</span><br><span class="line">179</span><br><span class="line">180</span><br><span class="line">181</span><br><span class="line">182</span><br><span class="line">183</span><br><span class="line">184</span><br><span class="line">185</span><br><span class="line">186</span><br><span class="line">187</span><br><span class="line">188</span><br><span class="line">189</span><br><span class="line">190</span><br><span class="line">191</span><br><span class="line">192</span><br><span class="line">193</span><br><span class="line">194</span><br><span class="line">195</span><br><span class="line">196</span><br><span class="line">197</span><br><span class="line">198</span><br><span class="line">199</span><br><span class="line">200</span><br><span class="line">201</span><br><span class="line">202</span><br><span class="line">203</span><br><span class="line">204</span><br><span class="line">205</span><br><span class="line">206</span><br><span class="line">207</span><br><span class="line">208</span><br><span class="line">209</span><br><span class="line">210</span><br><span class="line">211</span><br><span class="line">212</span><br><span class="line">213</span><br><span class="line">214</span><br><span class="line">215</span><br><span class="line">216</span><br><span class="line">217</span><br><span class="line">218</span><br><span class="line">219</span><br><span class="line">220</span><br><span class="line">221</span><br><span class="line">222</span><br><span class="line">223</span><br><span class="line">224</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> remove _</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span>+<span class="number">10</span>,M=<span class="number">2</span>*N;</span><br><span class="line"><span class="type">int</span> h[N],e[M],ne[M],w[M],idx,cnt,fa[N],top[N],nw[N],dep[N],tmp[N];</span><br><span class="line"><span class="type">int</span> id[N],sz[N],son[N];</span><br><span class="line"><span class="keyword">typedef</span> pair&lt;<span class="type">int</span>, <span class="type">int</span>&gt; PII;</span><br><span class="line">PII ab[N];</span><br><span class="line"><span class="type">int</span> n,x,y,a,b,c,m;</span><br><span class="line">string op;</span><br><span class="line"><span class="type">int</span> rt;</span><br><span class="line"><span class="comment">// struct node{</span></span><br><span class="line"><span class="comment">//     int sum,max,min,lazy;</span></span><br><span class="line"><span class="comment">// }t[N*4];</span></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">    <span class="type">int</span> sum,max,min,lazy;</span><br><span class="line">    <span class="type">int</span> ls,rs;</span><br><span class="line">}t[N*<span class="number">4</span>];</span><br><span class="line"><span class="type">int</span> root[N];</span><br><span class="line"><span class="type">int</span> color[N];</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">add</span><span class="params">(<span class="type">int</span> a,<span class="type">int</span> b,<span class="type">int</span> c)</span></span>{</span><br><span class="line">    e[++idx]=b,w[idx]=c,ne[idx]=h[a],h[a]=idx;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">dfs1</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> father)</span></span>{</span><br><span class="line">    dep[u]=dep[father]+<span class="number">1</span>,fa[u]=father,sz[u]=<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=h[u];i;i=ne[i]){</span><br><span class="line">        <span class="type">int</span> j=e[i];</span><br><span class="line">        <span class="keyword">if</span>(j==father)<span class="keyword">continue</span>;</span><br><span class="line">        <span class="built_in">dfs1</span>(j,u);</span><br><span class="line">        tmp[j]=w[i];</span><br><span class="line">        sz[u]+=sz[j];</span><br><span class="line">        <span class="keyword">if</span>(sz[son[u]]&lt;sz[j])son[u]=j;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">dfs2</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> t)</span></span>{</span><br><span class="line">    id[x]=++cnt,nw[cnt]=tmp[x],top[x]=t;</span><br><span class="line">    <span class="keyword">if</span>(son[x])<span class="built_in">dfs2</span>(son[x],t);</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=h[x];i;i=ne[i]){</span><br><span class="line">        <span class="type">int</span> j=e[i];</span><br><span class="line">        <span class="keyword">if</span>(j==fa[x]||j==son[x])<span class="keyword">continue</span>;</span><br><span class="line">        <span class="built_in">dfs2</span>(j,j);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    t[u].sum=t[t[u].ls].sum+t[t[u].rs].sum;</span><br><span class="line">    t[u].max=<span class="built_in">max</span>(t[t[u].ls].max,t[t[u].rs].max);</span><br><span class="line">    t[u].min=<span class="built_in">min</span>(t[t[u].ls].min,t[t[u].rs].min);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(t[u].lazy==<span class="number">0</span>)<span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">if</span>(!t[u].ls)t[u].ls=++rt;</span><br><span class="line">    <span class="keyword">if</span>(!t[u].rs)t[u].rs=++rt;</span><br><span class="line">    <span class="keyword">auto</span> &amp;L=t[t[u].ls];</span><br><span class="line">    <span class="keyword">auto</span> &amp;R=t[t[u].rs];</span><br><span class="line">    L.lazy^=<span class="number">1</span>,R.lazy^=<span class="number">1</span>;</span><br><span class="line">    L.sum=-L.sum,L.max=-L.max,L.min=-L.min;</span><br><span class="line">    R.sum=-R.sum,R.max=-R.max,R.min=-R.min;</span><br><span class="line">    <span class="built_in">swap</span>(L.max,L.min),<span class="built_in">swap</span>(R.max,R.min);</span><br><span class="line">    t[u].lazy=<span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"><span class="comment">// void build(int u=1,int l=1,int r=n){</span></span><br><span class="line"><span class="comment">//     t[u]={nw[l],nw[l],nw[l]};</span></span><br><span class="line"><span class="comment">//     if(l&gt;=r)return;</span></span><br><span class="line"><span class="comment">//     int mid=l+r&gt;&gt;1;</span></span><br><span class="line"><span class="comment">//     build(u&lt;&lt;1,l,mid),build(u&lt;&lt;1|1,mid+1,r);</span></span><br><span class="line"><span class="comment">//     pushup(u);</span></span><br><span class="line"><span class="comment">// }</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">modify</span><span class="params">(<span class="type">int</span> &amp;u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> i,<span class="type">int</span> k)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(!u)u=++rt;</span><br><span class="line">    <span class="keyword">if</span>(l==r){</span><br><span class="line">        t[u].sum=t[u].max=t[u].min=k;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">if</span>(i&lt;=mid)<span class="built_in">modify</span>(t[u].ls,l,mid,i,k);</span><br><span class="line">    <span class="keyword">else</span> <span class="built_in">modify</span>(t[u].rs,mid+<span class="number">1</span>,r,i,k);</span><br><span class="line">    <span class="built_in">pushup</span>(u);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">remove</span><span class="params">(<span class="type">int</span> &amp;u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> i,<span class="type">int</span> k)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(l==r){</span><br><span class="line">        t[u].max=<span class="number">-1e9</span>;</span><br><span class="line">        t[u].sum=<span class="number">0</span>;</span><br><span class="line">        t[u].min=<span class="number">1e9</span>;</span><br><span class="line">        t[u].lazy=<span class="number">0</span>;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="keyword">if</span>(i&lt;=mid)<span class="built_in">remove</span>(t[u].ls,l,mid,i,k);</span><br><span class="line">    <span class="keyword">else</span> <span class="built_in">remove</span>(t[u].rs,mid+<span class="number">1</span>,r,i,k);</span><br><span class="line">    <span class="built_in">pushup</span>(u);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">update</span><span class="params">(<span class="type">int</span> &amp;u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr,<span class="type">int</span> lazy=<span class="number">1</span>)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(l&gt;qr||r&lt;ql)<span class="keyword">return</span>;</span><br><span class="line">    <span class="keyword">if</span>(!u)u=++rt;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr){</span><br><span class="line">        t[u].sum=-t[u].sum;</span><br><span class="line">        t[u].max=-t[u].max;</span><br><span class="line">        t[u].min=-t[u].min;</span><br><span class="line">        <span class="built_in">swap</span>(t[u].max,t[u].min);</span><br><span class="line">        t[u].lazy^=<span class="number">1</span>;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)<span class="built_in">update</span>(t[u].ls,l,mid,ql,qr);</span><br><span class="line">    <span class="keyword">if</span>(qr&gt;mid)<span class="built_in">update</span>(t[u].rs,mid+<span class="number">1</span>,r,ql,qr);</span><br><span class="line">    <span class="built_in">pushup</span>(u);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qmax</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(!u)<span class="keyword">return</span> <span class="number">-1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;qr||r&lt;ql)<span class="keyword">return</span> <span class="number">-1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr)<span class="keyword">return</span> t[u].max;</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">-1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)ans=<span class="built_in">max</span>(ans,<span class="built_in">qmax</span>(t[u].ls,l,mid,ql,qr));</span><br><span class="line">    <span class="keyword">if</span>(qr&gt; mid)ans=<span class="built_in">max</span>(ans,<span class="built_in">qmax</span>(t[u].rs,mid+<span class="number">1</span>,r,ql,qr));</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qmin</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(!u)<span class="keyword">return</span> <span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;qr||r&lt;ql)<span class="keyword">return</span> <span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr)<span class="keyword">return</span> t[u].min;</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)ans=<span class="built_in">min</span>(ans,<span class="built_in">qmin</span>(t[u].ls,l,mid,ql,qr));</span><br><span class="line">    <span class="keyword">if</span>(qr&gt; mid)ans=<span class="built_in">min</span>(ans,<span class="built_in">qmin</span>(t[u].rs,mid+<span class="number">1</span>,r,ql,qr));</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qsum</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> ql,<span class="type">int</span> qr)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(!u)<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;qr||r&lt;ql)<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span>(l&gt;=ql&amp;&amp;r&lt;=qr)<span class="keyword">return</span> t[u].sum;</span><br><span class="line">    <span class="built_in">pushdown</span>(u);</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span>(ql&lt;=mid)ans+=<span class="built_in">qsum</span>(t[u].ls,l,mid,ql,qr);</span><br><span class="line">    <span class="keyword">if</span>(qr&gt; mid)ans+=<span class="built_in">qsum</span>(t[u].rs,mid+<span class="number">1</span>,r,ql,qr);</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="comment">/* 上面是线段树，下面是树链剖分*/</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">update</span><span class="params">(<span class="type">int</span> &amp;o,<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line">        <span class="keyword">if</span>(dep[top[x]]&lt;dep[top[y]])<span class="built_in">swap</span>(x,y);</span><br><span class="line">        <span class="built_in">update</span>(o,<span class="number">1</span>,n,id[top[x]],id[x]);</span><br><span class="line">        x=fa[top[x]];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(dep[x]&gt;dep[y])<span class="built_in">swap</span>(x,y);</span><br><span class="line">    <span class="keyword">if</span>(x!=y)<span class="built_in">update</span>(o,<span class="number">1</span>,n,id[x]+<span class="number">1</span>,id[y]);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qmax</span><span class="params">(<span class="type">int</span> o,<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">-1e9</span>;</span><br><span class="line">    <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line">        <span class="keyword">if</span>(dep[top[x]]&lt;dep[top[y]])<span class="built_in">swap</span>(x,y);</span><br><span class="line">        ans=<span class="built_in">max</span>(ans, <span class="built_in">qmax</span>(o,<span class="number">1</span>,n,id[top[x]],id[x]) );</span><br><span class="line">        x=fa[top[x]];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(dep[x]&gt;dep[y])<span class="built_in">swap</span>(x,y);</span><br><span class="line">    <span class="keyword">if</span>(x!=y)ans=<span class="built_in">max</span>(ans,<span class="built_in">qmax</span>(o,<span class="number">1</span>,n,id[x]+<span class="number">1</span>,id[y]));</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qmin</span><span class="params">(<span class="type">int</span> o,<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line">        <span class="keyword">if</span>(dep[top[x]]&lt;dep[top[y]])<span class="built_in">swap</span>(x,y);</span><br><span class="line">        ans=<span class="built_in">min</span>(ans, <span class="built_in">qmin</span>(o,<span class="number">1</span>,n,id[top[x]],id[x]));</span><br><span class="line">        x=fa[top[x]];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(dep[x]&gt;dep[y])<span class="built_in">swap</span>(x,y);</span><br><span class="line">    <span class="keyword">if</span>(x!=y)ans=<span class="built_in">min</span>(ans,<span class="built_in">qmin</span>(o,<span class="number">1</span>,n,id[x]+<span class="number">1</span>,id[y]));</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">qsum</span><span class="params">(<span class="type">int</span> o,<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">while</span>(top[x]!=top[y]){</span><br><span class="line">        <span class="keyword">if</span>(dep[top[x]]&lt;dep[top[y]])<span class="built_in">swap</span>(x,y);</span><br><span class="line">        ans+=<span class="built_in">qsum</span>(o,<span class="number">1</span>,n,id[top[x]],id[x]);</span><br><span class="line">        x=fa[top[x]];</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(dep[x]&gt;dep[y])<span class="built_in">swap</span>(x,y);</span><br><span class="line">    <span class="keyword">if</span>(x!=y)ans+=<span class="built_in">qsum</span>(o,<span class="number">1</span>,n,id[x]+<span class="number">1</span>,id[y]);</span><br><span class="line">    <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);</span><br><span class="line">    cin.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cin&gt;&gt;n;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;n;i++){</span><br><span class="line">        cin&gt;&gt;a&gt;&gt;b&gt;&gt;c;</span><br><span class="line">        a++,b++;</span><br><span class="line">        ab[i]={a,b};</span><br><span class="line">        <span class="built_in">add</span>(a,b,c);</span><br><span class="line">        <span class="built_in">add</span>(b,a,c);</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">dfs1</span>(<span class="number">1</span>,<span class="number">0</span>);</span><br><span class="line">    <span class="built_in">dfs2</span>(<span class="number">1</span>,<span class="number">1</span>);</span><br><span class="line">    <span class="comment">//build(1,1,n);</span></span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)color[i]=<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)<span class="built_in">modify</span>(root[color[i]],<span class="number">1</span>,n,id[i],tmp[i]);</span><br><span class="line">    cin&gt;&gt;m;</span><br><span class="line">    <span class="keyword">while</span>(m--){</span><br><span class="line">        cin&gt;&gt;op&gt;&gt;x&gt;&gt;y;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"C"</span>){</span><br><span class="line">            <span class="type">int</span> a=ab[x].first;</span><br><span class="line">            <span class="type">int</span> b=ab[x].second;</span><br><span class="line">            <span class="keyword">if</span>(dep[a]&lt;dep[b])<span class="built_in">swap</span>(a,b);</span><br><span class="line">            <span class="built_in">remove</span>(root[color[a]],<span class="number">1</span>,n,id[a],<span class="number">0</span>);</span><br><span class="line">            <span class="built_in">modify</span>(root[color[a]],<span class="number">1</span>,n,id[a],y);</span><br><span class="line">            <span class="keyword">continue</span>;</span><br><span class="line">        }</span><br><span class="line">        x++,y++;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"N"</span>)<span class="built_in">update</span>(root[color[x]],x,y);</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"SUM"</span>)cout&lt;&lt;<span class="built_in">qsum</span>(root[color[x]],x,y)&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"MAX"</span>)cout&lt;&lt;<span class="built_in">qmax</span>(root[color[x]],x,y)&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"MIN"</span>)cout&lt;&lt;<span class="built_in">qmin</span>(root[color[x]],x,y)&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>

<h2 id="线段树合并"><a href="#线段树合并" class="headerlink" title="线段树合并"></a>线段树合并</h2><p><img src="https://img-blog.csdnimg.cn/d4c9e6b86276495385a308af41f136ef.png" alt="在这里插入图片描述"></p>
<p>对每一个节点开一个权值线段树</p>
<p>用动态开点，不然会mle</p>
<p>而且不要直接#define int long long 只在关键变量开long long不然还是会MLE</p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="comment">// #define int long long</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e5</span>+<span class="number">10</span>,M=<span class="number">2</span>*N;</span><br><span class="line"><span class="type">int</span> h[N],e[M],ne[M],idx;</span><br><span class="line"><span class="type">int</span> n,m,c[N],root[N],cnt;</span><br><span class="line"><span class="type">long</span> <span class="type">long</span> ans[N];</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">    <span class="type">int</span> l,r;</span><br><span class="line">    <span class="type">long</span> <span class="type">long</span> sum;<span class="comment">//主要颜色的编号和</span></span><br><span class="line">    <span class="type">int</span> max;<span class="comment">//出现最多颜色的次数</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> ls tr[u].l</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rs tr[u].r</span></span><br><span class="line">}tr[N*<span class="number">100</span>];</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">add</span><span class="params">(<span class="type">int</span> a,<span class="type">int</span> b)</span></span>{</span><br><span class="line">    e[++idx]=b,ne[idx]=h[a],h[a]=idx;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    tr[u].max=<span class="built_in">max</span>(tr[ls].max,tr[rs].max);</span><br><span class="line">    <span class="keyword">if</span>(tr[ls].max==tr[rs].max)tr[u].sum=tr[ls].sum+tr[rs].sum;</span><br><span class="line">    <span class="keyword">if</span>(tr[ls].max &gt;tr[rs].max)tr[u].sum=tr[ls].sum;</span><br><span class="line">    <span class="keyword">if</span>(tr[ls].max &lt;tr[rs].max)tr[u].sum=tr[rs].sum;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    </span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">modify</span><span class="params">(<span class="type">int</span> &amp;o,<span class="type">int</span> l,<span class="type">int</span> r,<span class="type">int</span> i,<span class="type">int</span> k)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(!o)o=++cnt;</span><br><span class="line">    <span class="keyword">if</span>(l==r){</span><br><span class="line">        tr[o].max=<span class="number">1</span>;</span><br><span class="line">        tr[o].sum=k;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">if</span>(i&lt;=mid)<span class="built_in">modify</span>(tr[o].l,l,mid,i,k);</span><br><span class="line">    <span class="keyword">else</span> <span class="built_in">modify</span>(tr[o].r,mid+<span class="number">1</span>,r,i,k);</span><br><span class="line">    <span class="built_in">pushup</span>(o);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">merge</span><span class="params">(<span class="type">int</span> a,<span class="type">int</span> b,<span class="type">int</span> l,<span class="type">int</span> r)</span></span>{<span class="comment">//线段树合并</span></span><br><span class="line">    <span class="keyword">if</span>(!a)<span class="keyword">return</span> b;</span><br><span class="line">    <span class="keyword">if</span>(!b)<span class="keyword">return</span> a;<span class="comment">//哪个没有就返回另一个点的编号</span></span><br><span class="line">    <span class="keyword">if</span>(l==r){</span><br><span class="line">        tr[a].max+=tr[b].max;</span><br><span class="line">        <span class="keyword">return</span> a;</span><br><span class="line">    }</span><br><span class="line">    <span class="type">int</span> mid=l+r&gt;&gt;<span class="number">1</span>;</span><br><span class="line">    tr[a].l=<span class="built_in">merge</span>(tr[a].l,tr[b].l,l,mid);<span class="comment">//合并a，b的左儿子</span></span><br><span class="line">    tr[a].r=<span class="built_in">merge</span>(tr[a].r,tr[b].r,mid+<span class="number">1</span>,r);<span class="comment">//合并a，b的右儿子</span></span><br><span class="line">    <span class="built_in">pushup</span>(a);</span><br><span class="line">    <span class="keyword">return</span> a;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">cal</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> fa=<span class="number">0</span>)</span></span>{</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=h[u];i;i=ne[i]){</span><br><span class="line">        <span class="type">int</span> j=e[i];</span><br><span class="line">        <span class="keyword">if</span>(j==fa)<span class="keyword">continue</span>;</span><br><span class="line">        <span class="built_in">cal</span>(j,u);</span><br><span class="line">        root[u]=<span class="built_in">merge</span>(root[u],root[j],<span class="number">1</span>,n);</span><br><span class="line">    }</span><br><span class="line">    ans[u]=tr[root[u]].sum;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);cin.<span class="built_in">tie</span>(<span class="number">0</span>);cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cin&gt;&gt;n;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)cin&gt;&gt;c[i];</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;n;i++){</span><br><span class="line">        <span class="type">int</span> a,b;</span><br><span class="line">        cin&gt;&gt;a&gt;&gt;b;</span><br><span class="line">        <span class="built_in">add</span>(a,b);</span><br><span class="line">        <span class="built_in">add</span>(b,a);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)<span class="built_in">modify</span>(root[i],<span class="number">1</span>,n,c[i],c[i]);</span><br><span class="line">    <span class="built_in">cal</span>(<span class="number">1</span>);</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)cout&lt;&lt;ans[i]&lt;&lt;<span class="string">" "</span>;</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>
                
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